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Algebra Level 4

Find the largest possible product nmn\cdot m of two distinct positive integers nn and m,m, such that the equations (x+1)n=xn+1 (x+1)^n=x^n+1 and (x+1)m=xm+1(x+1)^m=x^m+1 have the same set of complex roots.

Details and assumptions

The multiplicities of the roots can, of course, be different, but each root of one equation is a root of the other.

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